Abstract
Conditionals are not only central items for knowledge representation, but also play an important part in belief revision, in particular when dealing with iterated belief revision. To handle conditional beliefs appropriately, epistemic states instead of propositional belief sets have to be considered. Within this framework, the preservation of conditional beliefs turns out to be a principal concern, corresponding to the paradigm of minimal propositional change to be found in AGM theory.
In this paper, we deal with the revision of epistemic states by conditional beliefs, thus extending the usual framework of only taking propositional or factual beliefs as new information. We present a thorough formalization of the principle of conditional preservation under revision for ordinal conditional functions, commonly regarded as appropriate representations of epistemic states. Though apparently quite simple and elementary, this formal principle will be shown to imply the postulates dealing with conditional preservation stated in other papers.
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References
C. E. Alchourrón, P. Gärdenfors, and P. Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50(2):510–530, 1985.
C. Boutilier and M. Goldszmidt. Revision by conditional beliefs. In Proceedings 11th National Conference on Artificial Intelligence (AAAI’93), pages 649–654, Washington, DC., 1993.
P. G. Calabrese. Deduction and inference using conditional logic and probability. In I. R. Goodman, M. M. Gupta, H. T. Nguyen, and G. S. Rogers, editors, Conditional Logic in Expert Systems, pages 71–100. Elsevier, North Holland, 1991.
A. Darwiche and J. Pearl. On the logic of iterated belief revision. Artificial Intelligence, 89:1–29, 1997.
B. DeFinetti. Theory of Probability, volume 1,2. John Wiley and Sons, New York, 1974.
D. Dubois and H. Prade. Conditioning, non-monotonic logic and non-standard uncertainty models. In I. R. Goodman, M. M. Gupta, H. T. Nguyen, and G. S. Rogers, editors, Conditional Logic in Expert Systems, pages 115–158. Elsevier, North Holland, 1991.
P. Gärdenfors. Knowledge in Flux: Modeling the Dynamics of Epistemic States. MIT Press, Cambridge, Mass., 1988.
M. Goldszmidt and J. Pearl. Qualitative probabilities for default reasoning, belief revision, and causal modeling. Artificial Intelligence, 84:57–112, 1996.
H. Katsuno and A. Mendelzon. Propositional knowledge base revision and minimal change. Artificial Intelligence, 52:263–294, 1991.
G. Kern-Isberner. Postulates for conditional belief revision. In Proceedings IJCAI-99. Morgan Kaufmann, 1999. (to appear).
W. Spohn. Ordinal conditional functions: a dynamic theory of epistemic states. In W. L. Harper and B. Skyrms, editors, Causation in Decision, Belief Change, and Statistics, II, pages 105-134. Kluwer Academic Publishers, 1988.
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Kern-Isberner, G. (1999). Following Conditional Structures of Knowledge. In: Burgard, W., Cremers, A.B., Cristaller, T. (eds) KI-99: Advances in Artificial Intelligence. KI 1999. Lecture Notes in Computer Science(), vol 1701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48238-5_10
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DOI: https://doi.org/10.1007/3-540-48238-5_10
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